Linear Operators: Spectral theory |
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Page 1290
... coefficients Pi are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) is a real function . If we use ...
... coefficients Pi are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) is a real function . If we use ...
Page 1435
... coefficients k " ) , ... , k ) , e ,, c ) , c ( 2 ) , can be determined by formally substituting the asymptotic expression for σ , in [ ** ] and comparing coefficients of z- " . Thus , in all cases in which we deal with a formal ...
... coefficients k " ) , ... , k ) , e ,, c ) , c ( 2 ) , can be determined by formally substituting the asymptotic expression for σ , in [ ** ] and comparing coefficients of z- " . Thus , in all cases in which we deal with a formal ...
Page 1486
... coefficients a , are periodic and have the same period . We can assume without loss of generality that this period is 1 ; thus a , ( t + 1 ) = a , ( t ) , = 0 , n . If follows immediately that all the coefficients of 7 are bounded ...
... coefficients a , are periodic and have the same period . We can assume without loss of generality that this period is 1 ; thus a , ( t + 1 ) = a , ( t ) , = 0 , n . If follows immediately that all the coefficients of 7 are bounded ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero